Problem 13.

  Two small beads having positive charges 25q and q are fixed at the opposite ends of a horizontal insulating rod, extending from the origin (the location of the larger charge) to the point x = d. A third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium?

Solution

Let us assume that the position of the third charge is x (the distance from the larger charge) and the charge of the third charge is Q. Then the equilibrium condition is: the net force is 0. This condition can be written as

From this equation we can find the distance x: